The problem asks us to evaluate two expressions. a) $-10^0$ b) $(\frac{4}{9})^{\frac{3}{2}}$

1. Problem Description

The problem asks us to evaluate two expressions.

a) $-10^0$

b) $(\frac{4}{9})^{\frac{3}{2}}$

2. Solution Steps

a) To evaluate $-10^0$, we need to remember that any number (except 0) raised to the power of 0 is

1. In this case, we have the negative sign in front of $10^0$. Therefore, $-10^0 = -(10^0) = -1$.

b) To evaluate $(\frac{4}{9})^{\frac{3}{2}}$, we can rewrite the expression as $(\sqrt{\frac{4}{9}})^3$.

First, we find the square root of $\frac{4}{9}$:

$\sqrt{\frac{4}{9}} = \frac{\sqrt{4}}{\sqrt{9}} = \frac{2}{3}$.

Now, we raise this result to the power of 3:

$(\frac{2}{3})^3 = \frac{2^3}{3^3} = \frac{8}{27}$.

3. Final Answer

a) $-1$

b) $\frac{8}{27}$